## Walking Speed

A persons natural walking speed is a result of the natural frequency of movement of their legs. We can treat a persons leg as a pendulum and find its natural frequency. The period of a pendulum of length\[l\]

is \[T=2 \pi \sqrt{\frac{l}{g}}\]

so the frequency is \[f= \frac{1}{T} =\frac{1}{2 \pi} \sqrt{\frac{g}{l}} \]

.If someone with a leg of length

\[l\]

takes \[f\]

strides per second, swinging their leg through an angle of 30 ° each time, then the distance moved in one stride is \[d=l \theta\]

and the distance moved in one second, the speed, is \[v=df=l \theta \frac{1}{2 \pi} \sqrt{\frac{g}{l}} = \frac{\theta}{2 \pi} \sqrt{lg}\]

.The length of a leg is about 0.9m and a person may swing their leg through an arc of 39°' or

\[\frac{\pi}{6}\]

.\[v=df= \frac{\theta}{2 \pi} \sqrt{lg}=\frac{\pi/6}{2 \pi} \sqrt{0.9 \times 9.8}= 0.25 m/s\]

.This is only an approximation. A comfortable walking speed is about 3 miles per hour or

\[\frac{3 \times 1609}{3600}= 1.34 m/s\]

.